A business travellers\' association rates hotels on a variety of factors includi

Question

A business travellers' association rates hotels on a variety of factors including price, cleanliness, services, and amenities to produce an overall score out of 100 for each hotel. Here are the ratings for 50 hotels in a major city. a) What score represents i) the 50^th percentile? ii) the 95^th percentile? b) What percentile corresponds to a rating of 50? c) The travellers' association lists hotels above the 90^th percentile as "highly recommended" and hotels between the 75^th and 90^th percentiles as "recommended." What are the minimum scores for the two levels of recommended hotels?

Explanation / Answer

(a) Arranging the numbers in ascending order:

39,41,42,44,48,50,50,51,53,55,56,56,57,58,59,60,60,60,62,63,65,65,66,67,68,68,68,70,71,73,73,74,74,75,76,77,78,78,79,80,81,81,84,85,86,87,89,91,94,96

n = 50

(i) 50th percentile :

p = 50

Index i = (p/100) X n = (50/100) X 50 = 25.

Since index i is integer, then 50th percentile is the average of ith and (i+1)th values. i.e., = average of 25th and 26th values = (68 + 68)/2 = 68.

(ii) 95th percentile:

index i = 47.5.

So, 95th percentile = 48th value = 91.

(b) Rating of 50 = 6th value.

So, percentile of 50 :

6 = (p/100)Xn = (p/100)X50 = p/2

So, p = 12

So, a rating of 50 corresponds to 12th percentile.

(c)

(i) minimum score for 90th percentile:

i = 45

So, 90th percentile = (86 + 87)/2 = 86.5

(ii) minimum score for 75th percentile:

i = 37.5

So, 75th percentile = 38th value = 78.

Minimum score for hotel between 75th and 90th percentile = 78.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.